Question 1100461: How am i to get the solution to the equation |x-3|=2x+1?
It says I am to end up with a extraneous solution, but I do not know what that means or how to get it.
Found 3 solutions by Alan3354, KMST, ankor@dixie-net.com:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How am i to get the solution to the equation |x-3|=2x+1?
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x-3 = 2x+1
x = 2x + 4
-x = 4
x = -4
Check:
|-4-3| = -7
|-7| = -7
NG
Absolute value cannot be negative.
--> extraneous solution
===============
-(x-3) = 2x+1
-x+3 = 2x+1
3 = 3x+1
3x = 2
x = 2/3
=================
Check:
|x-3|=2x+1
|(2/3 - 3)| = 4/3+1 = 7/3
|-7/3| = 7/3
No problem.
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Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! Maybe  , and then  ,
or maybe  and then  .
If ,
the equation simplifies to
 <-->  <-->  <-->  <-->  .
That is a solution of ,
but is it a solution of the original equation?
Let's check.
If ,  and  .
At the same time, if ,  .
Clearly, makes  true,
so  is a solution of .
What about the case when ?
Will that lead to another solution?
If ,
the equation simplifies to
 <-->  <-->  .
 is a solution to ,
but it is not a solution to the original equation.
It makes  ,  , and
 .
Clearly, if makes , and  ,
it is not a solution to .
we call it an extraneous solution.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! |x-3| = 2x+1
x - 3 = 2x + 1
-3 - 1 = 2x - x
-4 = x, an extraneous solution, as you can see if you substitute in the original equation
|-4 - 3| = 2(-4) + 1
|-7| = -8 + 1
Absolute is always positive
+7 does not = -7
:
Solution 2
|x - 3| = 2x + 1
x - 3 = -(2x + 1)
x - 3 = -2x - 1
x + 2x = -1 + 3
3x = 2
x = 2/3, this solution will work in the original equation
:
|(2/3)-3)| = 2(2/3) + 1
|- 7/3| = +7/3
+7/3 = +7/3
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